Problem: Simplify the following expression: $\sqrt{2}-\sqrt{32}+\sqrt{50}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{2}-\sqrt{32}+\sqrt{50}$ $= \sqrt{2}-\sqrt{16 \cdot 2}+\sqrt{25 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{2}-\sqrt{16} \cdot \sqrt{2}+\sqrt{25} \cdot \sqrt{2}$ $= \sqrt{2}-4\sqrt{2}+5\sqrt{2}$ Finally, simplify by combining the terms. $= ( 1 - 4 + 5 )\sqrt{2} = 2\sqrt{2}$